Method for the efficiency-corrected real-time quantification of nucleic acids

ABSTRACT

The present invention concerns a method for the quantification of a target nucleic acid in a sample comprising the following steps: (i) determination of the amplification efficiency of the target nucleic acid under defined amplification conditions, (ii) amplification of the target nucleic acid contained in the sample under the same defined reaction conditions, (iii) measuring the amplification in real-time, (iv) quantification of the original amount of target nucleic acid in the sample by correction of the original amount derived from step (iii) with the aid of the determined amplification efficiency. The efficiency correction of PCR reactions according to the invention for the quantification of nucleic acids can be used for absolute quantification with the aid of an external or internal standard as well as for relative quantification compared to the expression of housekeeping genes.

PRIOR ART

[0001] Methods for the quantification of nucleic acids are important inmany areas of molecular biology and in particular for moleculardiagnostics. At the DNA level such methods are used for example todetermine the copy numbers of gene sequences amplified in the genome.However, methods for the quantification of nucleic acids are usedespecially in connection with the determination of mRNA quantities sincethis is usually a measure for the expression of the respective codinggene.

[0002] If a sufficient amount of sample material is available, specialmRNAs can be quantified by conventional methods such as Northern Blotanalysis or RNAse protection assay methods. However, these methods arenot sensitive enough for sample material that is only available in smallamounts or for genes that are expressed very weakly.

[0003] The so-called RT-PCR is a much more sensitive method. In thismethod a single-stranded cDNA is firstly produced from the mRNA to beanalysed using a reverse transcriptase. Subsequently a double-strandedDNA amplification product is generated with the aid of PCR.

[0004] A distinction is made between two different variants of thismethod:

[0005] A In the so-called relative quantification the ratio of theexpression of a certain target RNA is determined relative to the amountof RNA of a so-called housekeeping gene which is assumed to beconstitutively expressed in all cells independent of the respectivephysiological status. Hence the mRNA is present in approximately thesame amount in all cells.

[0006] The advantage of this is that different initial qualities of thevarious sample materials and the process of RNA preparation has noinfluence on the particular result. However, an absolute quantificationis not possible with this method.

[0007] Alternatively the absolute amount of RNA used can be determinedwith the aid of standard nucleic acids of a known copy number andamplification of a corresponding dilution series of this standardnucleic acid. There are two alternatives:

[0008] When using external standards the standard and target nucleicacid are amplified in separate reaction vessels. In this case a standardcan be used with an identical sequence to the target nucleic acid.However, systematic errors can occur in this type of quantification ifthe RNA preparation to be analysed contains inhibitory components whichimpair the efficiency of the subsequent PCR reaction. Such errors can beexcluded by using internal standards i.e. by amplifying the standard andtarget nucleic acid in one reaction vessel. However, a disadvantage ofthis method is that standards have to be used that have differentsequences compared to the target nucleic acid to be analysed in order tobe able to distinguish between the amplification of the standard andtarget nucleic acid. This can in turn lead to a systematic error in thequantification since different efficiencies of the PCR amplificationcannot be excluded when the sequences are different.

[0009] PCR products can be quantified in two fundamentally differentways:

[0010] a) End Point Determination of the Amount of PCR Product Formed inthe Plateau Phase of the Amplification Reaction

[0011] In this case the amount of PCR product formed does not correlatewith the amount of the initial copy number since the amplification ofnucleic acids at the end of the reaction is no longer exponential andinstead a saturation is reached. Consequently different initial copynumbers exhibit identical amounts of PCR product formed. Therefore thecompetitive PCR or competitive RT-PCR method is usually used in thisprocedure. In these methods the specific target sequence is coamplifiedtogether with a dilution series of an internal standard of a known copynumber. The initial copy number of the target sequence is extrapolatedfrom the mixture containing an identical PCR product quantity ofstandard and target sequence (Zimmermann and Mannhalter, Bio-Techniques21:280-279, 1996). A disadvantage of this method is also thatmeasurement occurs in the saturation region of the amplificationreaction.

[0012] b) Kinetic Real-Time Quantification in the Exponential Phase ofPCR.

[0013] In this case the formation of PCR products is monitored in eachcycle of the PCR. The amplification is usually measured in thermocyclerswhich have additional devices for measuring fluorescence signals duringthe amplification reaction. A typical example of this is the RocheDiagnostics LightCycler (Cat. No. 2 0110468). The amplification productsare for example detected by means of fluorescent labelled hybridizationprobes which only emit fluorescence signals when they are bound to thetarget nucleic acid or in certain cases also by means of fluorescentdyes that bind to double-stranded DNA. A defined signal threshold isdetermined for all reactions to be analysed and the number of cycles Cprequired to reach this threshold value is determined for the targetnucleic acid as well as for the reference nucleic acids such as thestandard or housekeeping gene. The absolute or relative copy numbers ofthe target molecule can be determined on the basis of the Cp valuesobtained for the target nucleic acid and the reference nucleic acid(Gibson et al., Genome Research 6:995-1001; Bieche et al., CancerResearch 59:2759-2765, 1999; WO 97/46707; WO 97/46712; WO 97/46714).

[0014] In summary in all the described methods for the quantification ofa nucleic acid by PCR the copy number formed during the amplificationreaction is always related to the copy number formed of a referencenucleic acid which is either a standard or an RNA of a housekeepinggene. In this connection it is assumed that the PCR efficiency of thetarget and reference nucleic acid are not different.

[0015] Usually a PCR efficiency of 2.00 is assumed which corresponds toa doubling of the copy number per PCR cycle (User Bulletin No. 2 ABIPrism 7700, PE Applied Biosystems, 1997).

[0016] However, it has turned out that the real PCR efficiency can bedifferent from 2.00 since it is influenced by various factors such asthe binding of primers, length of the PCR product, G/C content andsecondary structures of the nucleic acid to be amplified and inhibitorsthat may be present in the reaction mixture as a result of the samplepreparation. This is particularly relevant when using heterologousreference nucleic acids e.g. in the relative quantification compared tothe expression of housekeeping genes.

[0017] The object of the present invention was therefore to providemethods for the quantification of nucleic acids which overcome thedisadvantages of the prior art as described above. The object of thepresent invention was in particular to provide methods for thequantification of nucleic acids in which a target nucleic acid isquantified independent of the amplification efficiencies of targetnucleic acid and reference nucleic.

BRIEF DESCRIPTIONS OF THE INVENTION

[0018] This object is achieved according to the invention by a methodfor the quantification of a target nucleic acid in a sample comprisingthe following steps:

[0019] a) Determining the amplification efficiency of the target nucleicacid under defined conditions.

[0020] b) Amplifying the target nucleic acid contained in the sampleunder the same reaction conditions.

[0021] c) Measuring the amplification in real-time.

[0022] d) Quantifying the original amount of target nucleic acid in thesample by correction of the original amount derived from step c) withthe aid of the determined amplification efficiency.

[0023] According to the invention this method can be used for relativequantification compared to the expression of housekeeping genes as wellas for absolute quantification.

[0024] A first aspect of the invention therefore concerns a method forquantifying a target nucleic acid in a sample compared to a referencenucleic acid comprising the following steps:

[0025] a) Determining the amplification efficiencies of the targetnucleic acid and reference nucleic acid under defined amplificationconditions

[0026] b) Amplifying the target nucleic acid contained in the sample aswell as the reference nucleic acid contained in the sample under thesame defined amplification conditions.

[0027] c) Measuring the amplification of the target nucleic acid andreference nucleic acid in real- time

[0028] d) Calculating the original ratio of target nucleic acid andreference nucleic acid in the sample by correcting the ratio derivedfrom step c) with the aid of the amplification efficiencies determinedin step a).

[0029] A second aspect of the present invention concerns a method forthe quantification of a target nucleic acid in a sample comprising thefollowing steps:

[0030] a) Determining the amplification efficiencies of the targetnucleic acid and of an internal or an external standard under definedamplification conditions

[0031] b) Amplifying the target nucleic acid contained in the sample aswell as the internal or external standard under the same definedreaction conditions

[0032] c) Measuring the amplification of the target nucleic acid andstandard in real-time

[0033] d) Calculating the original copy number in the sample bycorrecting the copy number derived from step c) with the aid of theamplification efficiencies determined in step a).

[0034] In all methods the amplification efficiencies are preferablydetermined by

[0035] a) preparing a dilution series of the target nucleic acid

[0036] b) amplifying the target nucleic acid under defined reactionconditions according to A, the amplification of the nucleic acids beingmeasured in real-time

[0037] c) setting a defined signal threshold value

[0038] d) determining the cycle number for each dilution at which thesignal threshold value is exceeded,

[0039] e) calculating the amplification efficiency based on thedetermined cycle numbers.

DETAILED DESCRIPTION OF THE INVENTION

[0040] The object of the invention is achieved by a method for thequantification of a target nucleic acid in a sample comprising thefollowing steps:

[0041] a) Determining the amplification efficiency of the target nucleicacid under defined conditions

[0042] b) Amplifying the target nucleic acid contained in the sampleunder the same reaction conditions.

[0043] c) Measuring the amplification in real-time

[0044] d) Quantifying the original amount of target nucleic acid in thesample by correcting the original amount derived from step c) with theaid of the determined amplification efficiency.

[0045] The importance of an efficiency correction will be illustrated byan error calculation. Table 1 shows a theoretical calculation of theaverage percentage error of the determined copy number in the case ofamplification efficiencies that are different from 2.00 as a function ofthe respective cycle number. The error is calculated according to theformula

percentage error=(2^(n) /E ^(n)−1)×100

[0046] in which E is the efficiency of the amplification and n is therespective cycle number at which the percentage error is determined.TABLE 1 Detection Cycle (n) PCR efficiency (E) 10 15 20 25 30 35 2.00 —— — — — — 1.97  16%  25%  35%    46%    57%    70% 1.95  29%  46%  66%   88%   113%    142% 1.90  67%  116%  179%   260%   365%    500% 1.80187%  385%  722%   1290%   2260%   3900% 1.70 408% 1045% 2480%   5710%13.000%  29.500% 1.60 920% 2740% 8570% 26.400% 80.700% 246.400%

[0047] The amplification efficiency can be determined by various methodsfor example by determining a function with which the measured signal isdetermined relative to the amplification of the target nucleic acid as afunction of the cycle time.

[0048] The amplification efficiency is preferably determined by a methodin which

[0049] a) a dilution series of a target nucleic acid is prepared

[0050] b) the target nucleic acid is amplified under defined reactionconditions as claimed in claim and the amplification of the nucleic acidis measured in real-time

[0051] c) a defined signal threshold value is set

[0052] d) for each dilution the cycle number Cp is determined at whichthe signal threshold value is exceeded

[0053] e) a logarithmic linear function of the copy number of targetnucleic acid used for the amplification is determined as a function ofthe cycle number at which the signal threshold value is exceeded

[0054] f) the amplification efficiency E is calculated according to

E=G ^(−a)

[0055] wherein a is determined as the first derivative of the functiondetermined in step e) and G is

[0056] the base number of the logarithm.

[0057] In a similar manner the amplification efficiency can also bedetermined by a method in which

[0058] a) a dilution series of the target nucleic acid is prepared

[0059] b) the target nucleic acid is amplified under defined reactionconditions as claimed in claim 1 and the amplification of the nucleicacid is measured in real-time

[0060] c) a defined signal threshold value is set

[0061] d) the cycle number Cp at which the signal threshold value isexceeded is determined for each dilution

[0062] e) a linear function of the cycle number determined in step d) isdetermined as a function of a logarithm of the copy number of targetnucleic acid used for the amplification and

[0063] f) the amplification efficiency E is calculated according to

E=G ^(−1/a)

[0064] wherein a is determined as the first derivative of the functiondetermined in step e) and

[0065] G is the base number of the logarithm.

[0066] Both preferred procedures have the advantage that a systematicerror cannot occur that results from determining the amplificationefficiency in a phase of the PCR reaction in which there is no longer anexponential amplification of the target nucleic acid (plateau phase).

[0067] However, it unexpectedly turned out that under certain conditionsthe amplification efficiency can also be dependent on the originalamount of target nucleic acid or it can change during the first cyclesof an amplification reaction that is still in the exponential phase. Asubject matter of the invention is thus also a method for theefficiency-corrected quantification of nucleic acids in which theefficiency of the amplification is determined by

[0068] a) preparing a dilution series of the target nucleic acid

[0069] b) amplifying the target nucleic acid under defined reactionconditions as claimed in claim 1 and measuring the amplification of thenucleic acid in real-time

[0070] c) setting a defined signal threshold value

[0071] d) determining the cycle number Cp at which the signal thresholdvalue is exceeded for each dilution

[0072] e) determining the amplification efficiency as a function of theamount of target nucleic acid.

[0073] This can for example be achieved by derivation of a continuouslydifferentiable function F(Cp) of the Cp values as a function of theoriginal copy number or vice versa. The function F(Cp)=log(concentration of the original copy number) can for example bestandardized by mathematical algorithms such as a polynomial fit of ahigher degree. The amplification efficiency E can then be determined bythe equation

E=G ^(−dF(Cp)/dCp)

[0074] in which dF/(Cp) is the derivative of the continuous function andG is the base number of the logarithm. A polynomial fit of the 4^(th)degree has proven to be particularly suitable within the sense of theinvention.

[0075] The efficiency-corrected quantification of nucleic acidsaccording to the invention can in principle be used for methods forabsolute quantification as well as for methods for relativequantification.

[0076] Hence a subject matter of the present invention in relation torelative quantification is also a method for the quantification of atarget nucleic acid in a sample relative to a reference nucleic acidcomprising the following steps:

[0077] a) Determination of the amplification efficiencies of the targetnucleic acid and of the reference nucleic acid under definedamplification conditions.

[0078] b) Amplification of the target nucleic acid contained in thesample as well as of the reference nucleic acid contained in the sampleunder the same defined amplification conditions.

[0079] c) Measurement of the amplification of the target nucleic acidand of the reference nucleic acid in real-time.

[0080] d) Calculation of the original ratio of target nucleic acid andreference nucleic acid in the sample by correcting the ratio derivedfrom step c) with the aid of the amplification efficiencies determinedin step a).

[0081] Such a method according to the invention eliminates on the onehand the influence of inhibitors that may be present in the examinedsample and, on the other hand, corrects errors which may occur as aresult of different amplification efficiencies of the target nucleicacid and reference nucleic acid.

[0082] Steps b) to d) are advantageously carried out in a parallelmixture containing a so-called calibrator sample. The calibrator sampleis a sample which contains the target nucleic acid and reference nucleicacid in a defined ratio that is constant for each measurement.Subsequently the ratio of the quotients determined for the sample andfor the calibrator sample is determined as a measure for the originalamount of target nucleic acid in the sample. This has the advantage thatin addition other systematic errors are eliminated that are due todifferences in the detection sensitivity of the target nucleic acid andreference nucleic acid. Such systematic errors can for example occur asa result of different hybridization properties of the hybridizationprobes or, in the case of fluorescent-labelled probes, differentexcitation efficiencies, quantum yields or coupling efficiencies of thedye to the probe. Therefore the sample to be tested and the calibratorsample must be analysed in each experiment with the same detectionagents i.e. with the same batch of fluorescent-labelled hybridizationprobes.

[0083] A special embodiment of relative quantification according to theinvention is a method for the quantification of a target nucleic acid ina sample relative to a reference nucleic acid comprising the followingsteps:

[0084] a) Determination of the amplification efficiencies of the targetnucleic acid and of the reference nucleic acid under definedamplification conditions

[0085] b) Amplification of the target nucleic acid contained in thesample and of the reference nucleic acid contained in the sample underthe same defined amplification conditions.

[0086] c) Measurement of the amplification of the target nucleic acidand of the reference nucleic acid in real time.

[0087] d) Determination of a defined signal threshold value.

[0088] e) Determination of the cycle numbers at which the signalthreshold value is in each case exceeded during the amplification of thetarget nucleic acid and the reference nucleic acid.

[0089] f) Calculation of the original ratio of target nucleic acid andreference nucleic acid in the sample according to the formula

N(T)₀ /N(R)₀ =E(R)^(n(R)) /E(T)^(n(T)), wherein

[0090] N(T)₀=the original amount of target DNA present in the sample

[0091] N(R)₀=the original amount of reference DNA present in the sample

[0092] E(R)=the amplification efficiency of the reference nucleic acid

[0093] n(R)=the cycle number of the reference nucleic acid measured instep e)

[0094] E(T)=the amplification efficiency of the target nucleic acid

[0095] n(T)=the cycle number of the target nucleic acid measured in stepe)

[0096] In this embodiment it is advantageous to carry out steps b), c),e) and f) with a calibrator sample in order to eliminate systematicerrors due to the detection of amplification products and subsequentlythe ratio of the quotients measured for the sample and for thecalibrator sample are determined as a measure for the original amount oftarget nucleic acid in the sample.

[0097] The ratio obtained in step f) is calculated according to theinvention as follows:

N(T)_(n) =N(T)₀ ×E(T)^(n(T))  (1)

N(R)_(n) =N(R)₀ ×E(R)^(n(R))  (2)

[0098] in which N(T)_(n)=the amount of target DNA at the signalthreshold value

[0099] and N(R)_(n)=the amount of reference DNA at the signal thresholdvalue

[0100] From (1) and (2) it follows that: $\begin{matrix}{\frac{{N(T)}_{n}}{{N(R)}_{n}} = \frac{{N(T)}_{0} \times {E(T)}^{n{(T)}}}{{N(R)}_{0} \times {E(R)}^{n{(R)}}}} & (3)\end{matrix}$

[0101] From this it follows that: $\begin{matrix}{\frac{{N(T)}_{0}}{{N(R)}_{0}} = \frac{{N(T)}_{n} \times {E(R)}^{n{(R)}}}{{N(R)}_{n} \times {E(T)}^{n{(T)}}}} & (4)\end{matrix}$

[0102] Due to the fact that an identical signal threshold value has beenset for the target and reference nucleic acid this may be approximatedto:

N(T)_(n) =N(R)_(n).

[0103] Under this condition and starting from equation (4) for theoriginal ratio of target nucleic acid and reference nucleic acid, thisresults in the equation

N(T)₀ /N(R)₀ =E(R)^(n(R)) /E(T)^(n(T))   (5)

[0104] However, this assumed approximation does not apply when targetnucleic acid and reference nucleic acid are detected with differentsensitivities. According to the invention it is therefore particularlyadvantageous to measure a calibrator sample in a parallel reaction andto determine the ratio of the quotients N(T)₀/N(R)₀ measured for thesample and for the calibrator sample as a measure for the originalamount of target nucleic acid in the sample. This results in thefollowing from equation (4) using the indices

[0105]_(A) for the sample to be analysed and

[0106]_(K) for the calibrator sample $\begin{matrix}{{\frac{{N(T)}_{0A}}{{N(R)}_{0A}}/\frac{{N(T)}_{0K}}{{N(R)}_{0K}}} = \frac{\frac{{N(T)}_{n\quad A} \times {E(R)}^{n\quad {A{(R)}}}}{{N(R)}_{n\quad A} \times {E(T)}^{n\quad {A{(T)}}}}}{\frac{{N(T)}_{nK} \times {E(R)}^{{nK}{(R)}}}{{N(R)}_{nK} \times {E(T)}^{{nK}{(T)}}}}} & (6)\end{matrix}$

[0107] Due to the fact that an identical signal threshold value has beenset for the sample to be analysed and for the calibrator sample and thatidentical agents are used to detect target and reference amplicons inthe sample and in the calibrator sample, the ratio of the quotientdetermined for the sample and for the calibrator sample is as follows:${\frac{{N(T)}_{n\quad A}}{{N(R)}_{n\quad A}}/\frac{{N(T)}_{nK}}{{N(R)}_{nK}}} = 1$

[0108] Hence the ratio of the quotients of the sample to be analysed andthe calibrator sample is: $\begin{matrix}{{\frac{{N(T)}_{0A}}{{N(R)}_{0A}}/\frac{{N(T)}_{0K}}{{N(R)}_{0K}}} = {{E(R)}^{{n\quad {A{(R)}}} - {{nK}{(R)}}}*{E(T)}^{{{nK}{(T)}} - {n\quad {A{(T)}}}}}} & (7)\end{matrix}$

[0109] Consequently a relative value can be obtained in this manner forthe original copy number of target nucleic acid in the sample in whichsystematic errors due to different amplification efficiencies as well asdue to different detection sensitivities have been eliminated. The onlyrequirement for the accuracy of the determined value is the justifiedassumption that under absolutely identical buffer conditions theamplification and detection efficiencies are also identical in thevarious reaction vessels.

[0110] Requirement for all methods according to the invention forrelative quantification is that the amplification efficiency of thetarget nucleic acid as well as the amplification efficiency of thereference nucleic acid are determined. Both of these determinations arepreferably carried out by the methods described above by determining thecycle number at which a certain signal threshold value is exceeded.

[0111] In a preferred embodiment of relative quantification the sampleis divided into two aliquots and the real-time measurement of theamplification of the target nucleic acid and reference nucleic acid iscarried out in separate reaction vessels. This prevents interferencebetween the amplification reactions of the target nucleic acid and thereference nucleic acid with regard to their efficiency for example bycompetition for deoxynucleotides or Taq polymerase. Furthermore thetarget nucleic acid and reference nucleic acid can be detected with thesame detection systems, for example with the same DNA binding dye.

[0112] Alternatively the real-time measurement of the amplification oftarget nucleic acid and reference nucleic acid can be carried out in onesample in the same reaction vessel using differently labelledhybridization probes. This is particularly advantageous when only smallamounts of sample material are available because the number of PCRreactions required is halved in this manner.

[0113] If it is intended to determine the absolute amount of targetnucleic acid to be detected in a sample, then the method for thequantification of a target nucleic acid in a sample comprises thefollowing steps

[0114] a) Determination of the amplification efficiencies of the targetnucleic acid and of an internal or external standard under definedamplification conditions.

[0115] b) Amplification of the target nucleic acid contained in thesample as well as of the internal or external standard under the samedefined reaction conditions.

[0116] c) Measurement of the amplification of the target nucleic acidand standard in real time

[0117] d) Calculation of the original copy number in the sample bycorrecting the copy number derived from step c) with the aid of theamplification efficiencies determined in step a).

[0118] The sequences of the target nucleic acid and standard nucleicacid are advantageously substantially identical. However, when selectingthe sequence for an internal standard it must be taken into account thatthe available detection system should be able to distinguish between thestandard and target nucleic acid. This can for example be achieved byusing hybridization probes with different labels for the detection ofthe target nucleic acid and internal standard. Ideally oligonucleotidesare used for this as detection probes which can be used to distinguishbetween minimal sequence differences such as point mutations.

[0119] An advantage of using an internal standard is that the inhibitorspresent in the sample also influence the amplification of the standard.Hence differences in the amplification efficiencies can be minimized.

[0120] In contrast the use of an external standard has the advantagethat the amplification reactions of the target nucleic acid and standardcannot competitively interfere with one another with regard to theirefficiency. Moreover the amplification products of the standard andtarget nucleic acid can be detected in parallel reactions with the aidof the same detection system for example with the same hybridizationprobe. A disadvantage is possible differences in the PCR efficienciesdue to inhibitors in the sample. However, errors in the quantificationcaused by this can be eliminated by the method described in thefollowing:

[0121] In a preferred embodiment for the absolute quantification of atarget nucleic acid in a sample the method according to the inventioncomprises the following steps:

[0122] a) Determination of the amplification efficiencies of the targetnucleic acid as well as of an internal or external standard underdefined amplification conditions

[0123] b) Amplification of the target nucleic acid contained in thesample as well as of the internal or external standard under the samedefined reaction conditions

[0124] c) Measurement of the amplification of target nucleic acid andstandard in real-time

[0125] d) Setting a defined signal threshold value

[0126] e) Determination of the cycle number during the amplification oftarget nucleic acid and standard at which the signal threshold value isexceeded

[0127] f) Determination of the original copy number N(T)₀ of the targetnucleic acid in the sample according to the formula

N(T)₀ =N(S)₀ *E(S)^(n(S)) /E(T)^(n(T))  (8) in which

[0128] N(S)₀=the original amount of standard used

[0129] E(S)=the amplification efficiency of the standard

[0130] n(S)=the cycle number of the standard measured in step e)

[0131] E(T)=the amplification efficiency of the standard

[0132] n(T)=the cycle number of the target nucleic acid measured in stepe).

[0133] In this case like the relative quantification, the amplificationefficiencies of the target nucleic acid and the internal standard arepreferably determined as described by determining the cycle number atwhich a certain signal threshold value is exceeded. According to theinvention N(T)₀ is calculated as follows:

N(T)_(n) =N(T)₀ *E(T)^(n(T))

and

N(S)_(n) =N(S)₀ *E(S)^(n(s))

[0134] Since an identical signal threshold value has been set for thetarget and standard nucleic acid this approximates to:

N(T)_(n) =N(S)n

[0135] Hence the original copy number of target nucleic acid present inthe sample is calculated according to the equation

N(T)₀ =N(S)₀ *E(S)^(n(s)) /E(T)^(n(T))  (8)

[0136] The invention in particular also concerns those embodiments ofthe described methods for the efficiency-corrected quantification ofnucleic acids in which the amplification products are detected byhybridization probes which can be labelled with a detectable componentin many different ways.

[0137] A prerequisite for the efficiency-corrected determination of theoriginal amount of a target nucleic acid and for the determination ofthe amplification efficiencies per se is to define signal thresholdvalues and subsequently determine the cycle number for the respectiveamplification reaction at which a certain signal threshold value isreached. The signal threshold value can be determined according to theprior art in various ways:

[0138] According to the prior art the signal threshold value can forexample be a signal which corresponds to a certain multiple of thestatistical variance of the background signal (ABI Prism 7700Application Manual, Perkin Elmer).

[0139] Alternatively the cycle number at which the signal thresholdvalue is exceeded can be determined according to the so-called “fitpoint above threshold” method (LightCycler Operator's Manual, B59-B68,Roche Molecular Biochemicals, 1999).

[0140] In a further embodiment the threshold value can be determined asa relative value instead of an absolute value when, independently of theabsolute value of the signal, the course of the amplification reactionis determined as a function of the cycle number and subsequently the nthderivative is calculated. In this case exceeding certain extremes can bedefined as exceeding a certain signal threshold value (EP ApplicationNo. 0016523.4). Hence this method of determining the threshold value isindependent of the absolute signal strength of for example afluorescence signal. Thus it is particularly suitable for thoseembodiments in which the target nucleic acid and reference nucleic acidare amplified in the same reaction vessel and are detected with the aidof different fluorescent labels. Methods have proven to be particularlysuitable for the efficiency-corrected quantification of PCR products inwhich the maximum of the second derivative is determined as a measurefor the signal threshold value.

[0141] The hybridization probes used for the methods according to theinvention are usually single-stranded nucleic acids such assingle-stranded DNA or RNA or derivatives thereof or alternatively PNAswhich hybridize at the annealing temperature of the amplificationreaction to the target nucleic acid. These oligonucleotides usually havea length of 20 to 100 nucleotides.

[0142] Depending on the detection format the label can be introduced onany ribose or phosphate group of the oligonucleotide. Labels at the 3′and 5′ end of the nucleic acid molecule are preferred.

[0143] The type of label must be detectable in the real-time mode of theamplification reaction. This is for example in principle also (but notonly) possible with the aid of labels that can be detected by NMR.

[0144] Methods are particularly preferred in which the amplified nucleicacids are detected with the aid of at least one fluorescent-labelledhybridization probe.

[0145] Many test procedures are possible for this. The following threedetection formats have proven to be particularly suitable in connectionwith the present invention:

[0146] a) FRET Hybridization Probes

[0147] For this test format 2 single-stranded hybridization probes areused simultaneously which are complementary to adjacent sites of thesame strand of the amplified target nucleic acid. Both probes arelabelled with different fluorescent components. When excited with lightof a suitable wavelength, a first component transfers the absorbedenergy to the second component according to the principle offluorescence resonance energy transfer such that a fluorescence emissionof the second component can be measured when both hybridization probesbind to adjacent positions of the target molecule to be detected.

[0148] Alternatively it is possible to use a fluorescent-labelled primerand only one labelled oligonucleotide probe (Bernard et al., AnalyticalBiochemistry 235, p. 1001-107 (1998)).

[0149] b) TaqMan Hybridization Probes

[0150] A single-stranded hybridization probe is labelled with twocomponents. When the first component is excited with light of a suitablewavelength, the absorbed energy is transferred to the second component,the so-called quencher, according to the principle of fluorescenceresonance energy transfer. During the annealing step of the PCRreaction, the hybridization probe binds to the target DNA and isdegraded by the 5′-3′ exonuclease activity of the Taq polymerase duringthe subsequent elongation phase. As a result the excited fluorescentcomponent and the quencher are spatially separated from one another andthus a fluorescence emission of the first component can be measured.

[0151] c) Molecular Beacons

[0152] These hybridization probes are also labelled with a firstcomponent and with a quencher, the labels preferably being located atboth ends of the probe. As a result of the secondary structure of theprobe, both components are in spatial proximity in solution. Afterhybridization to the target nucleic acid both components are separatedfrom one another such that after excitation with light of a suitablewavelength the fluorescence emission of the first component can bemeasured (Lizardi et al., U.S. Pat. No. 5,118,801).

[0153] In the described embodiments in which only the target nucleicacid or only the reference nucleic acid or an external standard isamplified in one reaction vessel in each case, the respectiveamplification product can also be detected according to the invention bya DNA binding dye which emits a corresponding fluorescence signal uponinteraction with the double-stranded nucleic acid after excitation withlight of a suitable wavelength. The dyes SybrGreen and SybrGold(Molecular Probes) have proven to be particularly suitable for thisapplication. Intercalating dyes can alternatively be used.

[0154] A subject matter of the invention are also kits that containappropriate agents to carry out the method according to the invention.According to the invention these agents are present in the kit invarious compositions. A kit preferably contains reagents such as forexample a reverse transcriptase for preparing a cDNA, DNA polymerase forthe amplification reaction, specific primers for the amplificationreaction and optionally also specific hybridization probes to detect theamplification product. As an alternative polymerases for a single-stepRT-PCR reaction can be present in the kit. It is also possible that akit according to the invention contains package inserts or diskscontaining files with previously determined amplification efficienciesfor defined amplification conditions. Finally the invention alsoconcerns a kit which additionally contains further reagents for thesynthesis and labelling of oligonucleotides such as fluorescentNHS-esters or fluorescent-labelled CPGs. Moreover a kit according to theinvention can optionally also contain a DNA which can be used as aninternal or external standard.

[0155] The invention is further elucidated by the following examples:

EXAMPLE 1 Amplification of Cytokeratin 20 (CK20) and Porphobilinogen(PBGD) cDNAs

[0156] RNA was isolated from the cell line HT-29 (ATCC) using aHighPure-RNA Restriction Kit (Roche Diagnostics GmbH). Aftersemi-quantitative spectrophotometric determination, the RNAconcentration was adjusted to 100 ng/μl in RNA-free water. Three serialsingle dilutions were prepared from this with RNA concentrations of 10ng, 1 ng and 100 pg/μl.

[0157] Total cDNA was prepared from these dilutions by reversetranscription under the following conditions: 1 x AMV reversetranscription buffer    1 mM of each deoxynucleoside triphosphate 0.0625mM randomized hexamers 10 u AMV reverse transcriptase 10 μl RNA Ad. 20μl water

[0158] All mixtures were incubated for 10 minutes at 25° C., 30 minutesat 42° C. and 5 minutes at 95° C. for the cDNA synthesis. Subsequentlythey were cooled to 4° C. A sample containing 10 ng/μl HT29 RNA was usedas a calibrator. Afterwards the amplification reaction was carried outwhich was measured in real-time in the FRET HybProbe format on aLightCycler instrument (Roche Diagnostics GmbH). Each reaction mixturewas amplified under the following conditions: 1 x fast start DNAhybridization probes buffer 1 x detection mix 2 μl cDNA Ad. 20 μl water

[0159] The 1× detection mix was composed of 0.5 μM forward and 0.5 μMreverse primers, each 0.2 μM fluorescein and LC-Red 640 labelledhybridization probes, 4 mM magnesium chloride and 0.005% Brij-35.

[0160] Primers having SEQ ID NO: 1 and SEQ ID NO:2 were used to amplifya CK20 sequence. The CK20 product was detected using a fluorescein probehaving SEQ ID NO:3 and a LC-Red 640 hybridization probe having SEQ IDNO:4. Primers having SEQ ID NO:5 and 6 were used to detect the PBGDsequence. PBGD was detected using a fluorescein-labelled hybridizationprobe having SEQ ID NO:7 and an LC-Red 640-labelled hybridization probehaving SEQ ID NO:8.

[0161] The reaction mixtures were firstly incubated for 10 minutes at95° C. in the presence of 5 mM magnesium chloride for the amplification.The actual amplification reaction was carried out for 50 cyclesaccording to the following scheme:

[0162] 10 sec. 95° C.

[0163] 10 sec. 60° C.

[0164] 5 sec. 72° C.

[0165] After each incubation at 60° C. a fluorescence measurement wascarried out according to the manufacturer's instructions. The signalthreshold value (Cp value) was determined as the maximum of the 2^(nd)derivative of the amplification reaction as a function of the cyclenumber.

EXAMPLE 2 Determination of the Efficiency of the Amplification of CK20and PBGD

[0166] A function was established to determine the efficiency in whichthe cycle number Cp determined for the respective concentration wasdetermined as a function of the decadic logarithm of the RNAconcentration used.

[0167] A linear function was calculated from this function by regressionanalysis with the aid of the LightCycler software. Starting from thisfunction the efficiency was determined according to the equation

efficiency=10^(−1/a)

[0168] wherein ^(a) is the gradient (1^(st) derivative) of thedetermined regression line. TABLE 2 Conc (ng) Log (ng) Cp-CK20 Cp-PBGD0.1 −1.0 35.73 38.73 1 0.0 30.13 33.59 10 1.0 24.20 28.63 Efficiency:1.491 1.578

[0169] The results obtained for CK20 and PBGD are shown in table 2. Theresult shows that on the one hand the efficiencies are considerablydifferent from 2.00 i.e. a doubling of the target nucleic acid does nottake place with each PCR cycle. On the other hand, the result shows thatthe efficiencies of the amplification of CK20 and PBGD differsignificantly from one another under otherwise identical conditions.

EXAMPLE 3 Determination of the Original Ratio of Target Nucleic Acid andReference Nucleic Acid With and Without Correction of the AmplificationEfficiency

[0170] Under the conditions described in example 1 the ratio determinedof the original amount of CK20 and PBGD should be independent of therespective amplified concentration of the sample material used. Hencethe determination of the ratio for various amounts of sample RNA wasused to check the effect of an efficiency correction on the basis of themeasured values that were obtained. In this case the ratio of CK20 toPBGD was determined according to the invention according to equation(5). On the one hand, the ratio was determined using the efficienciesobtained from example 2 and on the other hand with an assumedamplification efficiency of 2.00 for CK20 and for PGD. The results areshown in table 3: TABLE 3 N(T)_(o)/N(R)_(o) HT29 CP Cp N(T)_(o)/N(R)_(o)Efficiency (ng) CK20 PBGD Efficiency = 2 corrected 0.1 ng 35.73 38.738.00 29.68   1 ng 30.13 33.59 11.00 26.66  10 ng 24.20 28.63 21.56 29.66M: 13.52 28.66 SD: 7.12 1.74 % CV: 52.7% 6.1%

[0171] As can be seen from the table, the efficiency-corrected valuescalculated for the ratio of N(T)₀/N(R)₀ have a significantly lowerstandard deviation for the various amounts of sample RNA than theuncorrected values and a coefficient of variation of 6.1% compared to52.7%.

EXAMPLE 4 Efficiency-Correction When Using a Calibrator

[0172] Analogously to examples 1 and 2 amplification reactions werecarried out in the presence of 10 mM magnesium chloride. In this case anefficiency of 1.491 was determined for CK20 and an efficiency of 1.578was determined for PBGD. In addition the Cp values of a calibratorsample containing an unknown amount of HT-29 RNA was determined at 5 mMand 10 mM magnesium chloride. The measured data were used to determinethe quotients of the ratios of CK20 to PBGD between the samples analysedin each case and the appropriate calibrator according to equation (7).This determination was carried out on the one hand with an assumedefficiency of 2 for the amplification of CK20 and PBGD as well as, onthe other hand, with the aid of experimentally determined amplificationefficiencies. The result is shown in table 4. TABLE 4 T:R/C HT29 Cp CpT:R/C Efficiency MgCl₂ (ng) CK20 PBGD Efficiency corrected  5 mM 0.1 ng36.59 39.09 0.76 0.92  5 mM   1 ng 30.60 32.60 0.54 0.72  5 mM  10 ng25.19 27.95 0.91 0.95 calibrator Cal. 24.78 27.67 1.00 1.00 10 mM 0.1 ng35.73 38.73 0.39 1.04 10 mM   1 ng 30.13 33.59 0.53 0.93 10 mM  10 ng24.20 28.63 1.04 1.04 calibrator Cal. 24.01 28.38 1.00 1.00 M: 0.70 0.93SD: 0.26 0.10 % CV: 36.7% 11.1% T:R/C = Cp = measured cycle number$\begin{matrix}\begin{matrix}{M = m} \\{{SD} = {st}} \\{{\% \quad {CV}} = {cc}}\end{matrix} & {\frac{{N(T)}_{0A}}{{N(R)}_{0A}}/}\end{matrix}\frac{{N(T)}_{0A}}{{N(R)}_{0A}}$

[0173] As can be seen in table 4, the efficiency-corrected values have alower standard deviation (0.10) as well as a three-fold lowercoefficient of variation than the T:R/C values with an assumed PCRefficiency of 2.00. This result shows that an efficiency correctionaccording to the invention is also advantageous in quantifications inwhich a standardization with the aid of calibrators has already beencarried out.

EXAMPLE 5 Absolute Quantification of Plasmid DNA

[0174] A decadic dilution series of a plasmid containing the PSA gene of10⁹ to 10² copies was prepared for this purpose. At the same time asecond decadic dilution series with a plasmid containing the gene forTNF (tumour necrosis factor) with an unknown copy number of plasmid DNAwas prepared. Afterwards the PSA reaction mixtures were amplified on aLightCycler (Roche Diagnostics) under standard conditions using theprimers having SEQ ID NO:9 and 10 and the TNF reaction mixtures wereamplified using the primers having SEQ ID NO:11 and 12 (RocheDiagnostics LightCycler SybrGreen Mastermix, 5 mM final concentrationMgCl₂, 0.5 μM final concentration of each primer). The amplification wasmeasured in real-time using the DNA binding agent SybrGreenI (MolecularProbes) under standard conditions in which the evaluation was carriedout according to the manufacturer's instructions in the secondderivative mode.

[0175] The original copy number of the TNF plasmid was determined in twodifferent ways on the basis of the obtained data.

[0176] On the one hand a calibration line based on the PSA amplificationwas generated assuming the same amplification efficiency for PSA andTNF.

[0177] On the other hand the original copy number was determinedaccording to formula (8). Analogously to example 2 the amplificationefficiency for PSA and TNF was determined by calculating a regressionline according to the formula

E=10^(1/a)

[0178] wherein ^(a) denotes the increase (1^(st) derivative) of thecalculated regression line. In this case an amplification efficiency of2.03 was determined for PSA and an amplification efficiency of 2.13 wasdetermined for TNF.

[0179] The results of the two different quantification procedures areshown in table 5. A so-called dilution check was carried out as ameasure for the accuracy of the determination. The values denoteddilution check are calculated from the quotients of the copy numbersmeasured for the respective dilution of two dilution mixtures thatdiffer from one another by a factor of 10. Thus a value of 10.00 wouldbe expected as the ideal value. TABLE 5 Not efficiency correctedEfficiency corrected Determined Determined copy number copy numberDilution per dilution Dilution check per dilution Dilution check 130826128 10.10 27728632 12.12 10⁻¹ 3053000 13.82 2287050 14.98 10⁻²220900 7.19 152643 7.94 10⁻³ 30710 11.61 19227 13.89 10⁻⁴ 2646 8.55 13849.52 10⁻⁵ 309.5 7.61 145.4 8.76 10⁻⁶ 40.66 3.86 16.6 3.84 10⁻⁷ 10.54 4.3Mean: 8.96 10.16

[0180] As the result of the dilution check from table 5 shows, the meanof the efficiency-corrected data results in a value of 10.16, whereasthe mean of non-efficiency-corrected data results in a value of 8.96which is considerably further away from the ideal value of 10.00. Fromthis it follows that an efficiency correction is also advantageous forembodiments in which an absolute quantification of nucleic acids withthe aid of PCR is carried out.

1 12 1 20 DNA Homo sapiens 1 atcaagcagt ggtacgaaac 20 2 18 DNA Homosapiens 2 aggacacacc gagcattt 18 3 25 DNA Homo sapiens 3 attacagacaaattgaagag ctgcg 25 4 25 DNA Homo sapiens 4 agtcagatta aggatgctca actgc25 5 19 DNA Homo sapiens 5 gcggagccat gtctggtaa 19 6 20 DNA Homo sapiens6 ccagggtacg aggctttcaa 20 7 24 DNA Homo sapiens 7 gagagtgatt cgcgtgggtacccg 24 8 25 DNA Homo sapiens 8 agagccagct tgctcgcata cagac 25 9 22 DNAHomo sapiens 9 gaggagttct tgaccccaaa ga 22 10 18 DNA Homo sapiens 10tccagcgtcc agcacaca 18 11 20 DNA Homo sapiens 11 cctgccccaa tccctttatt20 12 21 DNA Homo sapiens 12 ggtttcgaag tggtggtctt g 21

1. Method for the quantification of a target nucleic acid in a samplecomprising the following steps: a) determination of the amplificationefficiency of the target nucleic acid under defined amplificationconditions b) amplification of the target nucleic acid contained in thesample under the same defined reaction conditions c) measuring theamplification in real-time d) quantification of the original amount oftarget nucleic acid in the sample by correction of the original amountderived from step c) with the aid of the determined amplificationefficiency.
 2. Method as claimed in claim 1, wherein the efficiency ofthe amplification is determined by a) preparing a dilution series of thetarget nucleic acid b) amplifying the target nucleic acid under definedreaction conditions as claimed in claim 1, the amplification of thenucleic acid being measured in real time c) determining a definedthreshold value d) determining the cycle number at which the signalthreshold value is exceeded for each dilution e) determining alogarithmic linear function of the copy number of target nucleic acidused for the amplification as a function of the cycle number at whichthe signal threshold value is exceeded and f) calculating theamplification efficiency E according to E=G ^(−a) wherein ^(a) isdetermined as the first derivative of the function determined in step e)and G is the base number of the logarithm.
 3. Method as claimed in claim1, wherein the efficiency of the amplification is determined by a)preparing a dilution series of the target nucleic acid b) amplifying thetarget nucleic acid under defined reaction conditions as claimed inclaim 1, the amplification of the nucleic acid being measured in realtime c) determining a defined signal threshold value d) determining thecycle number at which the signal threshold value is exceeded for eachdilution e) determining a linear function of the cycle number determinedin step d) as a function of a logarithm of the copy number of targetnucleic acid used for the amplification and f) calculating theamplification efficiency E according to E=G ^(−1/a) wherein ^(a) isdetermined as the first derivative of the function determined in step e)and G is the base number of the logarithm.
 4. Method as claimed in claim1 wherein the efficiency of the amplification is determined by a)preparing a dilution series of the target nucleic acid b) amplifying thetarget nucleic acid under defined reaction conditions as claimed inclaim 1, the amplification of the nucleic acid being measured in realtime c) determining a defined signal threshold value d) determining thecycle number at which the signal threshold value is exceeded for eachdilution e) determining the amplification efficiency as a function ofthe amount of target nucleic acid.
 5. Method for the quantification of atarget nucleic acid in a sample relative to a reference nucleic acidcomprising the following steps: a) determination of the amplificationefficiencies of the target nucleic acid and of the reference nucleicacid under defined amplification conditions b) amplification of thetarget nucleic acid contained in the sample and of the reference nucleicacid contained in the sample under the same defined reaction conditionsc) measuring the amplification of the target nucleic acid and of thereference nucleic acid in real time d) calculation of the original ratioof target nucleic acid and reference nucleic acid in the sample bycorrection of the ratio derived from step c) with the aid of theamplification efficiencies determined in step a).
 6. Method as claimedin claim 5, wherein steps b)-d) are additionally carried out using acalibrator sample and subsequently the ratio of the quotients determinedfor the sample and for the calibrator sample is determined as a measurefor the original amount of target nucleic acid in the sample.
 7. Methodfor the quantification of a target nucleic acid in a sample relative toa reference nucleic acid comprising the following steps: a)determination of the amplification efficiencies of the target nucleicacid and of the reference nucleic acid under defined amplificationconditions b) amplification of the target nucleic acid contained in thesample as well as of the reference nucleic acid contained in the sampleunder the same defined amplification conditions. c) measurement of theamplification of the target nucleic acid and of the reference nucleicacid in real time. d) determining a defined signal threshold value e)determining the cycle numbers at which the signal threshold value isexceeded in each case during the amplification of target nucleic acidand reference nucleic acid f) calculating the original ratio of targetnucleic acid and of reference nucleic acid in the sample according tothe following formula N(T)₀ /N(R)₀ =E(R)^(n(R)) /E(T)^(n(T)), in whichN(T)₀=the original amount of target DNA present in the sample N(R)₀=theoriginal amount of reference DNA present in the sample E(R)=theamplification efficiency of the reference nucleic acid n(R)=the cyclenumber of the reference nucleic acid measured in step e) E(T)=theamplification efficiency of the target nucleic acid n(T)=the cyclenumber of the target nucleic acid measured in step e).
 8. Method asclaimed in claim 6, wherein steps b), c), e) and f) are additionallycarried out using a calibrator sample and subsequently the ratio of thequotients determined for the sample and for the calibrator sample isdetermined as a measure for the original amount of target nucleic acidin the sample.
 9. Method as claimed in claims 5-8, wherein thedetermination of the amplification efficiency of the target nucleic acidand the determination of the amplification efficiency of the referencenucleic acid is carried out by a method as claimed in claims 2-4. 10.Method as claimed in claims 5-9, wherein the real-time measurement ofthe amplification of target nucleic acid and reference nucleic acid in asample is carried out in separate reaction vessels.
 11. Method asclaimed in claims 5-9, wherein the real-time measurement of theamplification of target nucleic acid and reference nucleic acid in asample is carried out in the same reaction vessel using differentlylabelled hybridization probes.
 12. Method for the quantification of atarget nucleic acid in a sample comprising the following steps: a)determination of the amplification efficiencies of the target nucleicacid and of an internal or external standard under defined amplificationconditions b) amplification of the target nucleic acid contained in thesample and of the internal or external standard under the same definedreaction conditions c) measuring the amplification of the target nucleicacid and of the standard in real time d) calculating the original copynumber in the sample by correction of the copy number derived from stepc) with the aid of the amplification efficiencies determined in step a).13. Method for the quantification of a target nucleic acid in a samplecomprising the following steps: a) determination of the amplificationefficiencies of the target nucleic acid and of an internal or externalstandard under defined amplification conditions b) amplification of thetarget nucleic acid contained in the sample as well as of the internalor external standard under the same defined reaction conditions. c)measurement of the amplification of the target nucleic acid and of thestandard in real time. d) determining a defined signal threshold valuee) determining the cycle numbers at which the signal threshold value isexceeded during the amplification of target nucleic acid and standard f)determining the original copy number N(T)₀ of target nucleic acid in thesample according to the formula N(T)₀ =N(S)₀ *E(S)^(n(s)) /E(T)^(n(T)),in which N(S)₀=the original amount of standard used E(S)=theamplification efficiency of the standard n(S)=the cycle number of thestandard measured in step e) E(T)=the amplification efficiency of thetarget nucleic acid n(T)=the cycle number of the target nucleic acidmeasured in step e).
 14. Method as claimed in claims 12-13 wherein theamplification efficiencies are determined as claimed in claims 2-4. 15.Method as claimed in claims 12-14 using an internal standard, whereinreal-time measurement of the amplification of the target nucleic acidand internal standard is carried out with differently labelledhybridization probes.
 16. Method as claimed in claims 1-15, wherein theamplified nucleic acids are detected with the aid of at least onefluorescent-labelled hybridization probe.
 17. Method as claimed in claim16, wherein the amplified nucleic acids are detected with the aid ofFRET hybridization probes, molecular beacons or TaqMan probes. 18.Method as claimed in claims 1-10 or 12-14, wherein the amplified nucleicacids are detected with the aid of a DNA-binding dye, preferably withSybrGreen I.
 19. Kit containing agents to carry out the method asclaimed in claims 1-18.